Two years ago Ghana's statistical service announced it was revising its GDP estimates upwards by over 60%, suggesting that in the previous estimates about US$13bn worth's of economic activity had been missed. As a result, Ghana was suddenly upgraded from a low to lower-middle-income country. In response, Todd Moss, the development scholar and blogger at the Center of Global Development in Washington DC, exclaimed: "Boy, we really don't know anything!"

Shanta Devarajan, the World Bank's Chief Economist for Africa, struck a more dramatic tone. In an address to a conference organised by Statistics South Africa, he called the current state of affairs "Africa's statistical tragedy".

How good are these numbers?

My book – Poor Numbers: how we are misled by African development statistics and what to do about it – presents a study of the production and use of African economic development statistics. All of the central questions in development revolve around the measure of the production and consumption of goods and services. This is expressed in an aggregate composite metric called the Gross Domestic Product, which is used to rank and rate the wealth and progress of nations. It is the most widely used measure of economic activity, yet little is known about how this metric is produced and misused in debates about African economic development.

For a number of years now I have been trying to answer the question: How good are these numbers? The short answer is that they are poor. This is not just a matter of technical accuracy – the arbitrariness of the quantification process produces observations with very large errors and levels of uncertainty. This "numbers game" has taken on a dangerously misleading air of accuracy, and the resulting figures are used to make critical decisions that allocate scarce resources. International development actors are making judgments based on erroneous statistics. Governments are not able to make informed decisions because existing data are too weak or the data they need do not exist.

How could the country be among the poorest in the world one day, and find itself amongst aspiring middle income countries the next?

To grasp this chain of events, a basic understanding of national accounting is necessary. GDP is typically calculated as a sum of the "value added" of the production of goods and services in all sectors of the economy. In order to compare one year's value added with another, and thus get an idea of whether the economy is expanding or contracting, a new set of sums for all the sectors are computed. In order for these two amounts to be comparable, they are expressed in constant prices. The easiest way of doing this, particularly if data are sparse, which they are at most African statistical offices, is to generate "base year" estimates for future level estimates.

When picking a base year the statistical office chooses a year when it has more information on the economy than normally available; such as data from a household, agricultural or industrial survey. The information from these survey instruments is added to the normally available administrative data to form a new GDP estimate. This new total is then weighted by sectors, thereafter other indicators and proxies are used to calculate new annual estimates.

The importance of the base year

The base year is very important in three respects. Firstly, the GDP estimates will be expressed in constant prices for the base year. Second, the index number applies, so that a sector that was very economically important in the base year will continue to appear very important despite structural changes that may have occurred since the last base year.

Conversely, sectors that were unimportant or not even existing will barely have an impact on the official statistics. Finally, the data sources and the use of proxies are set in the base year. Even when new information is becoming available, national accountants may be unwilling or unable to add this data to the GDP series. Thus, when the base year is out of date, the GDP series becomes an increasingly unreliable guide to interpreting real economic change. The IMF statistical division recommends a change of base year every fifth year.

In the case of Ghana, their previous base year was made in 1993. Quite obviously, the structure of the economy has changed radically since then, partly due to the introduction of new technologies, such as the mobile phone and partly due to economic policy, such as the continued liberalisation and importance of non-state delivery of services such as in tertiary education. Through some sample surveys and availability of administrative data, such as those derived from VAT, the statistical office was increasingly aware that they were underestimating the size of the Ghanaian economy. Ghana Statistical Services therefore requested the services of the IMF as early as in 2002, which contracted a consultant to undertake the rebasing and revision of GDP estimates.

What about the comparisons with other countries? How should we compare the income and growth of Ghana with Nigeria, Kenya or other economies in the region? The lack of comparability of data and methods in national accounting practices in Sub-Saharan Africa is disturbing. According to my own survey, only 10 of these countries have a base year that is less than a decade old. When I compared statistics available from the World Bank and those published by the national statistical agencies that actually compile the GDP statistics there was an alarming level of discrepancy. A comparison of the data published in other sources further added support to the conclusion that with the current uneven application of methods and poor availability of data, any ranking of countries according to GDP is misleading.

Nigerian revision pending

Meanwhile, in Nigeria an upward revision is pending. Their base year for the national accounts, 1990, is even more outdated than that of Ghana. According to reports from the National Bureau of Statistics (NBS), Nigeria plans to change its base year to 2008. It has been boldly announced that this could lead to a "huge jump" in GDP figures.

This radically challenges our current understanding of economic development in Nigeria and in Africa. According to the World Development Indicators' most recent data, the total GDP in 2010 was above $200bn (in current US$). Nigerian GDP, before the predicted revision, already accounts for 18% of sub-Saharan Africa's total (about $1,200bn). The reports in the media, from the IMF and the NBS all indicate that Nigeria's GDP will increase at least as much as it did in Ghana.

Let us be conservative and assume that the GDP in Nigeria merely doubles following the revision. This alone will mean that the GDP for the whole region increases by more than 15%. The value of the increase amounts to nothing less than 40 economies roughly the size of Malawi's. The knowledge that currently there are 40 "Malawis" unaccounted for in the Nigerian economy should raise a few eyebrows.

It is a real tragedy that the statistical capacities of sub-Saharan African economies are in such a poor state. African development statistics tell us less than we would like to think about income, poverty and growth in the region. One of the most urgent challenges in African economic development is to devise a strategy for improving statistical capacity. This system currently causes more confusion than enlightenment. However, governments, international organisations and independent analysts need these development statistics to track and monitor efforts at improving living conditions on the African continent.